Users' Mathboxes Mathbox for BJ < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >   Mathboxes  >  bj-spnfw Structured version   Visualization version   GIF version

Theorem bj-spnfw 31845
Description: Theorem close to a closed form of spnfw 1915. (Contributed by BJ, 12-May-2019.)
Assertion
Ref Expression
bj-spnfw ((∃𝑥𝜑𝜓) → (∀𝑥𝜑𝜓))

Proof of Theorem bj-spnfw
StepHypRef Expression
1 19.2 1879 . 2 (∀𝑥𝜑 → ∃𝑥𝜑)
21imim1i 61 1 ((∃𝑥𝜑𝜓) → (∀𝑥𝜑𝜓))
Colors of variables: wff setvar class
Syntax hints:  wi 4  wal 1473  wex 1695
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1713  ax-4 1728  ax-6 1875
This theorem depends on definitions:  df-bi 196  df-ex 1696
This theorem is referenced by: (None)
  Copyright terms: Public domain W3C validator